Question

A plant manager is considering buying additional stamping machines to accommodate increasing demand. The alternatives are to buy 1 machine, 2 machines, or 3 machines. The profits realized under each alternative are a function of whether their bid for a recent defense contract is accepted or not. The payoff table below illustrates the profits realized (in $000's) based on the different scenarios faced by the manager.

Alternative           Bid Accepted       Bid Rejected

Buy 1 machine         $10                        $5

Buy 2 machines        $30                        $4

Buy 3 machines        $40                        $2

Refer to the information above. Assume that based on historical bids with the defense contractor, the plant manager believes that there is a 65% chance that the bid will be accepted and a 35% chance that the bid will be rejected.

a. Which alternative should be chosen using the expected monetary value (EMV) criterion?

b. What is the expected value under certainty?

c. What is the expected value under perfect information (EVPI)?

(I need an Excel Spreadsheet)

Answer 1

a. Which alternative should be chosen using the expected monetary value (EMV) criterion?

b. What is the expected value under certainty?

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A                                 B                                 C

Alternative                 Bid accepted               Bid rejected

Machine 1                  10                                5

Machine 2                  30                                4

Machine 3                  40                                2        

=MAX(B2:B4)          =MAX(C2:C4)

Probabilities               0.65                             0.35 7

certainty                                                         =(B6*B5)+(C6*C5)   

Alternative                 Bid accepted    Bid rejected              Expected payoff under risk 1

Machine 1                  10                                5          =SUMPRODUCT(B11:C11,$B$15:$C$15)     

Machine 2                   30                                4          =SUMPRODUCT(B12:C12,$B$15:$C$15)

Machine 3                   40                                2          =SUMPRODUCT(B13:C13,$B$15:$C$15)

Probabilities                0.65                            0.35

Expected value under risk                                         =MAX(D11:D13) 18

Expected value of perfect information = Expected value under 20 uncertainty - Expected value under risk

=C7-D17

=E19*1000

A                                             B                                                             C

Alternative                        Bid accepted                                      Bid rejected

Machine 1                          $10                                                         $5

Machine 2                          $30                                                        $4

Machine 3                          $40                                                        $2          

                                                $40                                                        $5

Probabilities                      0.65                                                       0.35

Expected value under certainity                                                $27.75

Alternative                          Bid accepted                     Bid rejected        Expected payoff under risk

Machine 1                          $10                                        $5                           8.25

  Machine 2                         $30                                        $4                           20.9

  Machine 3                         $40                                         $2                          26.7

  Probabilities                     0.65                                        0.35

Expected value under risk                                                                            26.7

Expected value of perfect information = Expected value $1.05 20 under uncertainity - Expected value under risk I $1,050.00

c.  What is the expected value under perfect information (EVPI)?

b.